%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV493^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:37:22 AM UTC 2026
% Result : Theorem 152.03s 73.06s
% Output : Refutation 152.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 9
% Syntax : Number of formulae : 121 ( 17 unt; 0 typ; 5 def)
% Number of atoms : 785 ( 121 equ; 0 cnn)
% Maximal formula atoms : 15 ( 6 avg)
% Number of connectives : 1430 ( 165 ~; 185 |; 30 &;1024 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 133 ( 5 ^; 119 !; 4 ?; 133 :)
% ( 0 !>; 0 ?*; 0 @-; 5 @+)
% Comments :
%------------------------------------------------------------------------------
thf('type/realax/real_type',type,
'type/realax/real': $tType ).
thf('const/sets/inf_decl',type,
'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf('const/sets/IN_decl',type,
'const/sets/IN':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf('const/sets/FINITE_decl',type,
'const/sets/FINITE':
!>[TA: $tType] : ( ( TA > $o ) > $o ) ).
thf('const/sets/EMPTY_decl',type,
'const/sets/EMPTY':
!>[TA: $tType] : ( TA > $o ) ).
thf('const/realax/real_le_decl',type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(sk1_decl,type,
sk1: 'type/realax/real' > $o ).
thf(sk2_decl,type,
sk2: 'type/realax/real' ).
thf(sk3_decl,type,
sk3: ( 'type/realax/real' > $o ) > $o ).
thf(sk4_decl,type,
sk4: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(sk5_decl,type,
sk5: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(sk6_decl,type,
sk6: ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(sk1_def,definition,
( sk1
= ( @+[A: 'type/realax/real' > $o] :
~ ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
& ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
=> ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ A ) @ A )
& ! [B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ B ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: 'type/realax/real'] :
~ ( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ A ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: 'type/realax/real',B: 'type/realax/real' > $o] :
@+[C: 'type/realax/real'] :
~ ( ( 'const/sets/IN' @ 'type/realax/real' @ C @ B )
=> ( 'const/realax/real_le' @ A @ C ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: 'type/realax/real',B: 'type/realax/real' > $o] :
@+[C: 'type/realax/real'] :
~ ( ( 'const/sets/IN' @ 'type/realax/real' @ C @ B )
=> ( 'const/realax/real_le' @ A @ C ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: 'type/realax/real' > $o] :
@+[B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
& ! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
=> ( 'const/realax/real_le' @ B @ C ) ) ) ) ) ).
thf(1,conjecture,
! [A: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
& ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
=> ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ A ) @ A )
& ! [B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/INF_FINITE_') ).
thf(2,negated_conjecture,
~ ! [A: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
& ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
=> ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ A ) @ A )
& ! [B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [A: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
& ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
=> ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ A ) @ A )
& ! [B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
( ( 'const/sets/FINITE' @ 'type/realax/real' @ sk1 )
& ( sk1
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
& ( ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sk1 ) @ sk1 )
| ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 ) )
& ( ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sk1 ) @ sk1 )
| ~ ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ sk2 ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
'const/sets/FINITE' @ 'type/realax/real' @ sk1,
inference(cnfConj,[status(thm)],[8]) ).
thf(6,axiom,
! [A: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
& ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
=> ? [B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
& ! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
=> ( 'const/realax/real_le' @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/INF_FINITE_LEMMA_') ).
thf(31,plain,
! [A: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
& ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
=> ? [B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
& ! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
=> ( 'const/realax/real_le' @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(32,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
| ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ A ) @ A ) )
& ( ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
| ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
| ( 'const/realax/real_le' @ ( sk6 @ A ) @ B ) ) ),
inference(cnf,[status(esa)],[31]) ).
thf(34,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
| ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
| ( 'const/realax/real_le' @ ( sk6 @ A ) @ B ) ),
inference(cnfConj,[status(thm)],[32]) ).
thf(36,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
| ( 'const/realax/real_le' @ ( sk6 @ A ) @ B ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(1985,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ $true
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
| ( 'const/realax/real_le' @ ( sk6 @ A ) @ B )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sk1 )
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9,36]) ).
thf(1986,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
| ( 'const/realax/real_le' @ ( sk6 @ A ) @ B )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sk1 )
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ A ) ) ),
inference(simp,[status(thm)],[1985]) ).
thf(1987,plain,
! [A: 'type/realax/real'] :
( ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
| ( 'const/realax/real_le' @ ( sk6 @ sk1 ) @ A ) ),
inference(pattern_uni,[status(thm)],[1986:[bind(A,$thf( sk1 )),bind(B,$thf( B ))]]) ).
thf(2278,plain,
! [A: 'type/realax/real'] :
( ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
| ( 'const/realax/real_le' @ ( sk6 @ sk1 ) @ A ) ),
inference(simp,[status(thm)],[1987]) ).
thf(10,plain,
( sk1
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(13,plain,
( sk1
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(31660,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
| ( 'const/realax/real_le' @ ( sk6 @ sk1 ) @ A ) ),
inference(simplifyReflect,[status(thm)],[2278,13]) ).
thf(33,plain,
! [A: 'type/realax/real' > $o] :
( ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
| ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ A ) @ A ) ),
inference(cnfConj,[status(thm)],[32]) ).
thf(35,plain,
! [A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ A ) @ A ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(1290,plain,
! [A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ $true
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ A ) @ A )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sk1 )
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9,35]) ).
thf(1291,plain,
! [A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ A ) @ A )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sk1 )
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ A ) ) ),
inference(simp,[status(thm)],[1290]) ).
thf(1292,plain,
( ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1291:[bind(A,$thf( sk1 ))]]) ).
thf(1484,plain,
'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ sk1 ) @ sk1,
inference(simplifyReflect,[status(thm)],[1292,13]) ).
thf(12,plain,
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sk1 ) @ sk1 )
| ~ ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ sk2 ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(1493,plain,
( ~ $true
| ~ ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ sk2 )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sk1 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1484,12]) ).
thf(1494,plain,
( ~ ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ sk2 )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sk1 ) @ sk1 ) ) ),
inference(simp,[status(thm)],[1493]) ).
thf(1534,plain,
( ~ ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ sk2 )
| ( ( sk6 @ sk1 )
!= ( 'const/sets/inf' @ sk1 ) )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[1494]) ).
thf(1561,plain,
( ~ ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ sk2 )
| ( ( sk6 @ sk1 )
!= ( 'const/sets/inf' @ sk1 ) ) ),
inference(simp,[status(thm)],[1534]) ).
thf(31943,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
| ~ $true
| ( ( sk6 @ sk1 )
!= ( 'const/sets/inf' @ sk1 ) )
| ( ( 'const/realax/real_le' @ ( sk6 @ sk1 ) @ A )
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[31660,1561]) ).
thf(31944,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
| ( ( sk6 @ sk1 )
!= ( 'const/sets/inf' @ sk1 ) )
| ( ( 'const/realax/real_le' @ ( sk6 @ sk1 ) @ A )
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ sk2 ) ) ),
inference(simp,[status(thm)],[31943]) ).
thf(32019,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
| ( ( sk6 @ sk1 )
!= ( 'const/sets/inf' @ sk1 ) )
| ( ( sk6 @ sk1 )
!= ( 'const/sets/inf' @ sk1 ) )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[31944]) ).
thf(32047,plain,
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 )
| ( ( sk6 @ sk1 )
!= ( 'const/sets/inf' @ sk1 ) ) ),
inference(simp,[status(thm)],[32019]) ).
thf(3,axiom,
! [A: 'type/realax/real' > $o] :
( ( ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
& ? [B: 'type/realax/real'] :
! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
=> ( 'const/realax/real_le' @ B @ C ) ) )
=> ( ! [B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ B ) )
& ! [B: 'type/realax/real'] :
( ! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
=> ( 'const/realax/real_le' @ B @ C ) )
=> ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/INF_') ).
thf(14,plain,
! [A: 'type/realax/real' > $o] :
( ( ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
& ? [B: 'type/realax/real'] :
! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
=> ( 'const/realax/real_le' @ B @ C ) ) )
=> ( ! [B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ B ) )
& ! [B: 'type/realax/real'] :
( ! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
=> ( 'const/realax/real_le' @ B @ C ) )
=> ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,plain,
! [D: 'type/realax/real',C: 'type/realax/real',B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk4 @ B @ A ) @ A )
| ( sk3 @ A ) )
& ( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/realax/real_le' @ B @ ( sk4 @ B @ A ) )
| ( sk3 @ A ) )
& ( ~ ( sk3 @ A )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
| ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ C ) )
& ( ~ ( sk3 @ A )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ D @ A ) @ A )
| ( 'const/realax/real_le' @ D @ ( 'const/sets/inf' @ A ) ) )
& ( ~ ( sk3 @ A )
| ~ ( 'const/realax/real_le' @ D @ ( sk5 @ D @ A ) )
| ( 'const/realax/real_le' @ D @ ( 'const/sets/inf' @ A ) ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(19,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk4 @ B @ A ) @ A )
| ( sk3 @ A ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(25,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk4 @ B @ A ) @ A )
| ( sk3 @ A ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(376,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk4 @ B @ A ) @ A )
| ( sk3 @ A )
| ( ( 'const/sets/EMPTY' @ 'type/realax/real' )
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[25,13]) ).
thf(377,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk4 @ B @ A ) @ A )
| ( sk3 @ A )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[376]) ).
thf(378,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk4 @ A @ sk1 ) @ sk1 )
| ( sk3 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[377:[bind(A,$thf( sk1 )),bind(B,$thf( B ))]]) ).
thf(476,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk4 @ A @ sk1 ) @ sk1 )
| ( sk3 @ sk1 ) ),
inference(simp,[status(thm)],[378]) ).
thf(20,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/realax/real_le' @ B @ ( sk4 @ B @ A ) )
| ( sk3 @ A ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(21,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/realax/real_le' @ B @ ( sk4 @ B @ A ) )
| ( sk3 @ A ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(70,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( 'const/realax/real_le' @ B @ ( sk4 @ B @ A ) )
| ( sk3 @ A )
| ( ( 'const/sets/EMPTY' @ 'type/realax/real' )
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[21,13]) ).
thf(71,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( 'const/realax/real_le' @ B @ ( sk4 @ B @ A ) )
| ( sk3 @ A )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[70]) ).
thf(72,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ A @ ( sk4 @ A @ sk1 ) )
| ( sk3 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[71:[bind(A,$thf( sk1 )),bind(B,$thf( B ))]]) ).
thf(90,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ A @ ( sk4 @ A @ sk1 ) )
| ( sk3 @ sk1 ) ),
inference(simp,[status(thm)],[72]) ).
thf(31661,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
| ~ $true
| ( sk3 @ sk1 )
| ( ( 'const/realax/real_le' @ ( sk6 @ sk1 ) @ A )
!= ( 'const/realax/real_le' @ B @ ( sk4 @ B @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[31660,90]) ).
thf(31662,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
| ( sk3 @ sk1 )
| ( ( 'const/realax/real_le' @ ( sk6 @ sk1 ) @ A )
!= ( 'const/realax/real_le' @ B @ ( sk4 @ B @ sk1 ) ) ) ),
inference(simp,[status(thm)],[31661]) ).
thf(31663,plain,
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( sk4 @ ( sk6 @ sk1 ) @ sk1 ) @ sk1 )
| ( sk3 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[31662:[bind(A,$thf( sk4 @ ( sk6 @ sk1 ) @ sk1 )),bind(B,$thf( sk6 @ sk1 ))]]) ).
thf(32417,plain,
! [A: 'type/realax/real'] :
( ( sk3 @ sk1 )
| ~ $true
| ( sk3 @ sk1 )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk4 @ A @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ ( sk4 @ ( sk6 @ sk1 ) @ sk1 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[476,31663]) ).
thf(32418,plain,
! [A: 'type/realax/real'] :
( ( sk3 @ sk1 )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk4 @ A @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ ( sk4 @ ( sk6 @ sk1 ) @ sk1 ) @ sk1 ) ) ),
inference(simp,[status(thm)],[32417]) ).
thf(32419,plain,
sk3 @ sk1,
inference(pattern_uni,[status(thm)],[32418:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(17,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk3 @ A )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ B @ A ) @ A )
| ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(22,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk3 @ A )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ B @ A ) @ A )
| ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(32691,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ $true
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ B @ A ) @ A )
| ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) )
| ( ( sk3 @ sk1 )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[32419,22]) ).
thf(32692,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ B @ A ) @ A )
| ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) )
| ( ( sk3 @ sk1 )
!= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[32691]) ).
thf(32693,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ A @ sk1 ) @ sk1 )
| ( 'const/realax/real_le' @ A @ ( 'const/sets/inf' @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[32692:[bind(A,$thf( sk1 )),bind(B,$thf( B ))]]) ).
thf(32731,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ A @ sk1 ) @ sk1 )
| ( 'const/realax/real_le' @ A @ ( 'const/sets/inf' @ sk1 ) ) ),
inference(simp,[status(thm)],[32693]) ).
thf(16,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk3 @ A )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
| ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ B ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(24,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk3 @ A )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
| ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ B ) ),
inference(simp,[status(thm)],[16]) ).
thf(1499,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk3 @ A )
| ~ $true
| ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ B )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1484,24]) ).
thf(1500,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk3 @ A )
| ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ B )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ B @ A ) ) ),
inference(simp,[status(thm)],[1499]) ).
thf(1501,plain,
( ~ ( sk3 @ sk1 )
| ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ ( sk6 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[1500:[bind(A,$thf( sk1 )),bind(B,$thf( sk6 @ sk1 ))]]) ).
thf(5,axiom,
! [A: 'type/realax/real',B: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ A @ B )
& ( 'const/realax/real_le' @ B @ A ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realax/REAL_LE_ANTISYM_') ).
thf(28,plain,
! [A: 'type/realax/real',B: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ A @ B )
& ( 'const/realax/real_le' @ B @ A ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(29,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ A @ B )
& ( 'const/realax/real_le' @ B @ A ) )
= ( A = B ) ),
inference(cnf,[status(esa)],[28]) ).
thf(30,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ A @ B )
& ( 'const/realax/real_le' @ B @ A ) )
= ( A = B ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(1621,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ~ ( sk3 @ sk1 )
| ( ( $true
& ( 'const/realax/real_le' @ B @ A ) )
= ( A = B ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ ( sk6 @ sk1 ) )
!= ( 'const/realax/real_le' @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1501,30]) ).
thf(1622,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ~ ( sk3 @ sk1 )
| ( ( 'const/realax/real_le' @ B @ A )
= ( A = B ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ ( sk6 @ sk1 ) )
!= ( 'const/realax/real_le' @ A @ B ) ) ),
inference(simp,[status(thm)],[1621]) ).
thf(1623,plain,
( ~ ( sk3 @ sk1 )
| ( ( 'const/realax/real_le' @ ( sk6 @ sk1 ) @ ( 'const/sets/inf' @ sk1 ) )
= ( ( 'const/sets/inf' @ sk1 )
= ( sk6 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[1622:[bind(A,$thf( 'const/sets/inf' @ sk1 )),bind(B,$thf( sk6 @ sk1 ))]]) ).
thf(32639,plain,
( ~ $true
| ( ( 'const/realax/real_le' @ ( sk6 @ sk1 ) @ ( 'const/sets/inf' @ sk1 ) )
= ( ( 'const/sets/inf' @ sk1 )
= ( sk6 @ sk1 ) ) ) ),
inference(rewrite,[status(thm)],[1623,32419]) ).
thf(32640,plain,
( ( 'const/realax/real_le' @ ( sk6 @ sk1 ) @ ( 'const/sets/inf' @ sk1 ) )
= ( ( 'const/sets/inf' @ sk1 )
= ( sk6 @ sk1 ) ) ),
inference(simp,[status(thm)],[32639]) ).
thf(88423,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ A @ sk1 ) @ sk1 )
| ( ( 'const/sets/inf' @ sk1 )
= ( sk6 @ sk1 ) )
| ( ( 'const/realax/real_le' @ A @ ( 'const/sets/inf' @ sk1 ) )
!= ( 'const/realax/real_le' @ ( sk6 @ sk1 ) @ ( 'const/sets/inf' @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[32731,32640]) ).
thf(88424,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ ( sk6 @ sk1 ) @ sk1 ) @ sk1 )
| ( ( 'const/sets/inf' @ sk1 )
= ( sk6 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[88423:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(88646,plain,
( ( ( sk6 @ sk1 )
= ( 'const/sets/inf' @ sk1 ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ ( sk6 @ sk1 ) @ sk1 ) @ sk1 ) ),
inference(lifteq,[status(thm)],[88424]) ).
thf(11,plain,
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sk1 ) @ sk1 )
| ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(1497,plain,
( ~ $true
| ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sk1 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1484,11]) ).
thf(1498,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sk1 ) @ sk1 ) ) ),
inference(simp,[status(thm)],[1497]) ).
thf(1536,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 )
| ( ( sk6 @ sk1 )
!= ( 'const/sets/inf' @ sk1 ) )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[1498]) ).
thf(1545,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 )
| ( ( sk6 @ sk1 )
!= ( 'const/sets/inf' @ sk1 ) ) ),
inference(simp,[status(thm)],[1536]) ).
thf(89074,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ ( sk6 @ sk1 ) @ sk1 ) @ sk1 )
| ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 )
| ( ( 'const/sets/inf' @ sk1 )
!= ( 'const/sets/inf' @ sk1 ) )
| ( ( sk6 @ sk1 )
!= ( sk6 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[88646,1545]) ).
thf(89075,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ ( sk6 @ sk1 ) @ sk1 ) @ sk1 )
| ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 )
| ( ( sk6 @ sk1 )
!= ( sk6 @ sk1 ) ) ),
inference(simp,[status(thm)],[89074]) ).
thf(89076,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ ( sk6 @ sk1 ) @ sk1 ) @ sk1 )
| ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[89075:[]]) ).
thf(90019,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 )
| ~ $true
| ( 'const/realax/real_le' @ ( sk6 @ sk1 ) @ A )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ ( sk6 @ sk1 ) @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[89076,31660]) ).
thf(90020,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 )
| ( 'const/realax/real_le' @ ( sk6 @ sk1 ) @ A )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ ( sk6 @ sk1 ) @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 ) ) ),
inference(simp,[status(thm)],[90019]) ).
thf(90021,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 )
| ( 'const/realax/real_le' @ ( sk6 @ sk1 ) @ ( sk5 @ ( sk6 @ sk1 ) @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[90020:[bind(A,$thf( sk5 @ ( sk6 @ sk1 ) @ sk1 ))]]) ).
thf(18,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk3 @ A )
| ~ ( 'const/realax/real_le' @ B @ ( sk5 @ B @ A ) )
| ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(23,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk3 @ A )
| ~ ( 'const/realax/real_le' @ B @ ( sk5 @ B @ A ) )
| ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(96515,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 )
| ~ ( sk3 @ A )
| ~ $true
| ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) )
| ( ( 'const/realax/real_le' @ ( sk6 @ sk1 ) @ ( sk5 @ ( sk6 @ sk1 ) @ sk1 ) )
!= ( 'const/realax/real_le' @ B @ ( sk5 @ B @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[90021,23]) ).
thf(96516,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 )
| ~ ( sk3 @ A )
| ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) )
| ( ( 'const/realax/real_le' @ ( sk6 @ sk1 ) @ ( sk5 @ ( sk6 @ sk1 ) @ sk1 ) )
!= ( 'const/realax/real_le' @ B @ ( sk5 @ B @ A ) ) ) ),
inference(simp,[status(thm)],[96515]) ).
thf(96517,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 )
| ~ ( sk3 @ sk1 )
| ( 'const/realax/real_le' @ ( sk6 @ sk1 ) @ ( 'const/sets/inf' @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[96516:[bind(A,$thf( sk1 )),bind(B,$thf( sk6 @ sk1 ))]]) ).
thf(124108,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 )
| ~ $true
| ( ( 'const/sets/inf' @ sk1 )
= ( sk6 @ sk1 ) ) ),
inference(rewrite,[status(thm)],[96517,32640,32419]) ).
thf(124109,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 )
| ( ( 'const/sets/inf' @ sk1 )
= ( sk6 @ sk1 ) ) ),
inference(simp,[status(thm)],[124108]) ).
thf(124110,plain,
( ( ( sk6 @ sk1 )
= ( 'const/sets/inf' @ sk1 ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 ) ),
inference(lifteq,[status(thm)],[124109]) ).
thf(124206,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 )
| ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 )
| ( ( 'const/sets/inf' @ sk1 )
!= ( 'const/sets/inf' @ sk1 ) )
| ( ( sk6 @ sk1 )
!= ( sk6 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[124110,1545]) ).
thf(124207,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 )
| ( ( sk6 @ sk1 )
!= ( sk6 @ sk1 ) ) ),
inference(simp,[status(thm)],[124206]) ).
thf(124208,plain,
'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1,
inference(pattern_uni,[status(thm)],[124207:[]]) ).
thf(124812,plain,
( ~ $true
| ( ( sk6 @ sk1 )
!= ( 'const/sets/inf' @ sk1 ) ) ),
inference(rewrite,[status(thm)],[32047,124208]) ).
thf(124813,plain,
( ( sk6 @ sk1 )
!= ( 'const/sets/inf' @ sk1 ) ),
inference(simp,[status(thm)],[124812]) ).
thf(89415,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ ( sk6 @ sk1 ) @ sk1 ) @ sk1 )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 )
| ( ( 'const/sets/inf' @ sk1 )
!= ( 'const/sets/inf' @ sk1 ) )
| ( ( sk6 @ sk1 )
!= ( sk6 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[88646,32047]) ).
thf(89416,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ ( sk6 @ sk1 ) @ sk1 ) @ sk1 )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 )
| ( ( sk6 @ sk1 )
!= ( sk6 @ sk1 ) ) ),
inference(simp,[status(thm)],[89415]) ).
thf(89417,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ ( sk6 @ sk1 ) @ sk1 ) @ sk1 )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[89416:[]]) ).
thf(91926,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 )
| ~ $true
| ( 'const/realax/real_le' @ ( sk6 @ sk1 ) @ A )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ ( sk6 @ sk1 ) @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[89417,31660]) ).
thf(91927,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 )
| ( 'const/realax/real_le' @ ( sk6 @ sk1 ) @ A )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ ( sk6 @ sk1 ) @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 ) ) ),
inference(simp,[status(thm)],[91926]) ).
thf(91928,plain,
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ sk2 @ sk1 )
| ( 'const/realax/real_le' @ ( sk6 @ sk1 ) @ ( sk5 @ ( sk6 @ sk1 ) @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[91927:[bind(A,$thf( sk5 @ ( sk6 @ sk1 ) @ sk1 ))]]) ).
thf(124808,plain,
( ~ $true
| ( 'const/realax/real_le' @ ( sk6 @ sk1 ) @ ( sk5 @ ( sk6 @ sk1 ) @ sk1 ) ) ),
inference(rewrite,[status(thm)],[91928,124208]) ).
thf(124809,plain,
'const/realax/real_le' @ ( sk6 @ sk1 ) @ ( sk5 @ ( sk6 @ sk1 ) @ sk1 ),
inference(simp,[status(thm)],[124808]) ).
thf(129175,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk3 @ A )
| ~ $true
| ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) )
| ( ( 'const/realax/real_le' @ ( sk6 @ sk1 ) @ ( sk5 @ ( sk6 @ sk1 ) @ sk1 ) )
!= ( 'const/realax/real_le' @ B @ ( sk5 @ B @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[124809,23]) ).
thf(129176,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk3 @ A )
| ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) )
| ( ( 'const/realax/real_le' @ ( sk6 @ sk1 ) @ ( sk5 @ ( sk6 @ sk1 ) @ sk1 ) )
!= ( 'const/realax/real_le' @ B @ ( sk5 @ B @ A ) ) ) ),
inference(simp,[status(thm)],[129175]) ).
thf(129177,plain,
( ~ ( sk3 @ sk1 )
| ( 'const/realax/real_le' @ ( sk6 @ sk1 ) @ ( 'const/sets/inf' @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[129176:[bind(A,$thf( sk1 )),bind(B,$thf( sk6 @ sk1 ))]]) ).
thf(135396,plain,
( ~ $true
| ( ( 'const/sets/inf' @ sk1 )
= ( sk6 @ sk1 ) ) ),
inference(rewrite,[status(thm)],[129177,32640,32419]) ).
thf(135397,plain,
( ( 'const/sets/inf' @ sk1 )
= ( sk6 @ sk1 ) ),
inference(simp,[status(thm)],[135396]) ).
thf(135398,plain,
( ( sk6 @ sk1 )
= ( 'const/sets/inf' @ sk1 ) ),
inference(lifteq,[status(thm)],[135397]) ).
thf(135412,plain,
( ( 'const/sets/inf' @ sk1 )
!= ( 'const/sets/inf' @ sk1 ) ),
inference(rewrite,[status(thm)],[124813,135398]) ).
thf(135413,plain,
$false,
inference(simp,[status(thm)],[135412]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV493^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.09/0.22 % Computer : n016.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 15:58:04 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.88/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/1.01 % [INFO] Parsing done (206ms).
% 1.25/1.02 % [INFO] Running in sequential loop mode.
% 2.18/1.44 % [INFO] eprover registered as external prover.
% 2.18/1.45 % [INFO] Scanning for conjecture ...
% 2.39/1.56 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.39/1.60 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.56/1.62 % [INFO] Problem is higher-order (TPTP THF).
% 2.56/1.62 % [INFO] Type checking passed.
% 2.56/1.63 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 152.03/73.05 % [INFO] Killing All external provers ...
% 152.03/73.05 % Time passed: 72683ms (effective reasoning time: 72022ms)
% 152.03/73.05 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 152.03/73.06 % Axioms used in derivation (3): thm/sets/INF_FINITE_LEMMA_, thm/sets/INF_, thm/realax/REAL_LE_ANTISYM_
% 152.03/73.06 % No. of inferences in proof: 116
% 152.03/73.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 72683 ms resp. 72022 ms w/o parsing
% 152.43/73.15 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 152.43/73.15 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------